$ \left(\dfrac{1}{25}\right)^{-\frac{7}{2}}$
Answer: $= 25^{\frac{7}{2}}$ $= \left(25^{\frac{1}{2}}\right)^{7}$ To simplify $25^{\frac{1}{2}}$ , figure out what goes in the blank: $\left(? \right)^{2}=25$ To simplify $25^{\frac{1}{2}}$ , figure out what goes in the blank: $\left({5}\right)^{2}=25$ so $ 25^{\frac{1}{2}}=5$ So $25^{\frac{7}{2}}=\left(25^{\frac{1}{2}}\right)^{7}=5^{7}$ $= 5^{7}$ $= 5\cdot5\cdot 5\cdot 5\cdot 5\cdot 5\cdot 5$ $= 25\cdot5\cdot 5\cdot 5\cdot 5\cdot 5$ $= 125\cdot5\cdot 5\cdot 5\cdot 5$ $= 625\cdot5\cdot 5\cdot 5$ $= 3125\cdot5\cdot 5$ $= 15625\cdot5$ $= 78125$